A conventional gasoline engine is retrofitted to operate as a bi-fuel engine using Hydrogen gas as a primary fuel and gasoline as a secondary fuel at various acceptable air fuel ratios while avoiding forbidden air fuel ratios. The engine is preferably operated to burn Hydrogen fuel in a charged mode and lean mode at certain acceptable air fuel ratios where relatively little NOx emissions occur. When additional power or acceleration is requested, processor controlled fuel injectors are operated to inject relatively small amounts of gasoline into the engine resulting in a fuel mixture that prevents increases in NOx emissions as the processor operates at a stoichiometric air fuel ratio where a catalytic converter is best able to reduce harmful emissions. The injection of the liquid gasoline fuel to the gaseous Hydrogen fuel reduces the temperature of the fuels significantly and reduces or eliminates backfiring tendency of the engine.